A time-varying distribution parameter system space-time modeling method, device and equipment and medium for adaptive continuous learning

Abstract

This invention discloses an adaptive continuous learning spatiotemporal modeling method, apparatus, device, and medium for time-varying distributed parameter systems. The invention constructs an initial spatiotemporal prediction model using offline data. Upon entering the online phase, it quantifies the spatiotemporal nonstationarity of the system in real time and adaptively generates a spatiotemporal forgetting factor using a multi-criteria inference mechanism. This dynamically matches the model update rhythm with the variable-scale time-varying rhythm of the system dynamics, solving the problem that a fixed learning rate is difficult to adapt to multi-scale time-varying characteristics. Through a spatiotemporal collaborative replay learning mechanism, it consolidates historical core spatiotemporal dynamic modes by recalling them, overcoming the catastrophic forgetting phenomenon in continuous spatiotemporal learning. It repeats the online distributed parameter system data acquisition and dynamic model update steps until the online phase ends, achieving accurate tracking and long-term knowledge retention of time-varying spatiotemporal dynamics. This significantly improves the prediction accuracy and robustness of distributed parameter systems in complex nonstationary environments.

Description

Technical Field

[0001] This invention relates to the field of prediction of industrial distributed parameter systems, and in particular to a spatiotemporal modeling method, apparatus, equipment and medium for time-varying distributed parameter systems based on adaptive continuous learning. Background Technology

[0002] In process industries (such as chemical, metallurgical, and energy), the internal states of key production equipment, such as chemical reactors and metallurgical volatilization kilns, exhibit continuous spatial distribution and dynamic evolution over time, constituting typical distributed parameter systems (DPS). Unlike traditional lumped parameter systems, the states of DPS are often described by partial differential equations (PDEs), possessing infinite-dimensional characteristics. Against the backdrop of the intelligent upgrading needs of process industries, achieving high-precision modeling and prediction of DPS has direct engineering application value for process optimization, improving production efficiency, energy conservation and emission reduction, and ensuring operational safety.

[0003] Due to the inherent complexity and infinite-dimensionality of distributed parameter systems, establishing simplified models that accurately describe the spatiotemporal dynamics of the system while facilitating optimized control has always been a major challenge and core research direction in this field. However, traditional modeling methods rely on offline dataset training to obtain predictive models with fixed structures and parameters. Such static models struggle to adapt to the latest spatiotemporal dynamics of the system during online operation, leading to discrepancies between the model and the actual spatiotemporal dynamics, and consequently, prediction failure. To address this, existing technologies employ online update strategies based on sliding time windows or fixed forgetting factors, attempting to track the latest dynamics of the system by continuously introducing new data and discarding old data. However, these methods have significant shortcomings: First, existing online update strategies typically use fixed window lengths or globally uniform update weights, while the spatiotemporal evolution of distributed parameter systems often exhibits multi-timescale characteristics. Rigid update mechanisms struggle to simultaneously track rapidly changing time-varying conditions and maintain accuracy in steady-state conditions. Second, a simple sliding window mechanism forces the forgetting of historical data during model updates, preventing the model from effectively reusing existing knowledge when the system reproduces historical dynamic patterns, requiring relearning and causing fluctuations in predictive performance. Therefore, designing a continuous learning modeling method that can both adaptively track current time-varying dynamics and effectively maintain core historical knowledge is a pressing problem that needs to be solved. Summary of the Invention

[0004] The main objective of this invention is to provide an adaptive continuous learning spatiotemporal modeling method, apparatus, device, and medium for time-varying distributed parameter systems. This invention aims to solve the technical bottlenecks of existing online modeling technologies when facing complex non-stationary dynamics, such as the inability of fixed update strategies to match the multi-scale time-varying characteristics of the system, and the "catastrophic forgetting" dilemma caused by the forced discarding of historical data, which leads to the failure of system state prediction.

[0005] To achieve the above objectives, this invention provides an adaptive continuous learning spatiotemporal modeling method for time-varying distributed parameter systems. This method is applied to the modeling and analysis of distributed parameter systems in process industries, including chemical, metallurgical, and energy industries. The method includes the following steps:

[0006] The system collects offline stage state data of the distributed parameter system and performs KL decomposition on the offline stage state data to obtain spatial basis functions and time coefficient matrices. The offline stage state data is the spatiotemporal state data of the system under stable operating conditions collected by multiple spatial point sensors. The offline stage state data includes time series data of temperature, humidity, concentration, flow rate and / or pressure.

[0007] A spatiotemporal prediction model is constructed based on the spatial basis function and the time coefficient matrix. The spatiotemporal prediction model includes a time coefficient predictor and a spatial prediction model.

[0008] In response to the distributed parameter system being in the online phase, online phase status data is collected. A spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis is used to perform multi-scale spatiotemporal nonstationarity analysis on the online phase status data. By calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain, a spatiotemporal forgetting factor that matches the current dynamic rate of change is adaptively generated. The online phase status data is the spatiotemporal status data of the system under dynamic operating conditions collected by multiple spatial point sensors. The online phase status data includes time series data of temperature, humidity, concentration, flow rate and / or pressure.

[0009] The model update weights are determined based on the spatiotemporal forgetting factor. The spatiotemporal prediction model is dynamically updated based on the model update weights and the coupled generative spatiotemporal replay learning mechanism. The process of collecting online stage state data is then performed. The spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis is used to perform multi-scale spatiotemporal nonstationarity analysis on the online stage state data. The steps of adaptively generating a spatiotemporal forgetting factor that matches the current dynamic rate of change by calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain are repeated until the distribution parameter system ends the online stage. The spatiotemporal replay learning mechanism generates pseudo-samples by querying the degree of matching with historical data and mixes them with the online stage state data to generate spatiotemporal data. The spatiotemporal data is used for updating the spatiotemporal prediction model.

[0010] The distributed parameter system is modeled and analyzed based on the dynamically updated spatiotemporal prediction model.

[0011] Optionally, the spatiotemporal forgetting factor includes a temporal forgetting factor and a spatial forgetting factor; in response to the distributed parameter system being in the online stage, online stage state data is collected, and a spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis is used to perform multi-scale spatiotemporal nonstationarity analysis on the online stage state data. Furthermore, by calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain, a spatiotemporal forgetting factor adaptively generates a factor matching the current dynamic rate of change, including:

[0012] In response to the distributed parameter system being in the online phase, online phase status data is collected, which includes DPS status data within multiple time windows under the online state;

[0013] Spatiotemporal nonstationarity analysis is performed on the online stage state data to obtain spatiotemporal nonstationarity indices of DPS state data within a time window. The spatiotemporal nonstationarity indices include spatial projection reconstruction error and time prediction residual.

[0014] A fuzzy mapping based on spatiotemporal nonstationary indices is constructed to divide the numerical ranges of the spatial projection reconstruction error and the time prediction residual into multiple fuzzy subsets covering different intervals.

[0015] The values ​​of spatial projection reconstruction error and time prediction residual obtained from the online stage are input into the preset membership function to calculate the membership values ​​of the values ​​belonging to each fuzzy subset, so as to convert the rigid scalar into two independent spatiotemporal fuzzy membership vectors.

[0016] The spatiotemporal fuzzy membership vector is input into the fuzzy inference engine, and the corresponding spatial adjustment rules and temporal adjustment rules are activated respectively to infer the temporal forgetting factor and spatial forgetting factor.

[0017] Optionally, the spatiotemporal nonstationarity analysis process includes:

[0018] The spatial projection reconstruction error on the subspace formed by the online phase state data and the spatial basis function is calculated to quantify the degree of structural variation of the system's spatial distribution modes.

[0019] The prediction model for the time coefficient matrix is ​​used to calculate the time prediction residual for the time coefficient at the current moment, in order to quantify the degree of dynamic variation in the system's time evolution. The spatial projection reconstruction error and the time prediction residual are calculated using the following formulas:

[0020]

[0021]

[0022] Where SVC represents the spatial projection reconstruction error, TVC represents the temporal prediction residual, W represents the time window length, M represents the number of time sampling points, and N represents the number of spatial sampling points. This represents the first step after reconstruction using existing spatial basis functions. The value at each spatial location Indicates the first The values ​​of the original DPS state data at each spatial location. This represents the original time coefficient matrix. Represents the time coefficient matrix for prediction. Indicates spatial location ,time The original DPS state value at that location, Indicates spatial location ,time The predicted DPS state value at the location.

[0023] Optionally, the membership function includes:

[0024]

[0025] in, , and These represent the membership levels of the time variation coefficient to low, medium, and high values, respectively. It refers to fuzzy membership functions. , , , , , , , and These are the parameters of the fuzzy membership function.

[0026] Optionally, the step of determining model update weights based on the spatiotemporal forgetting factor, and dynamically updating the spatiotemporal prediction model based on the model update weights and the coupled generative spatiotemporal replay learning mechanism, includes:

[0027] A historical spatiotemporal dynamic library is constructed based on the DPS status data matrix during the offline phase;

[0028] The current feature trajectory is analyzed time-by-time from the online window data, where the online window data is a matrix of DPS state data collected during the online phase within the window time, and the current feature trajectory is composed of data features from multiple moments within the window time.

[0029]

[0030] in, This represents online window data. The feature trajectory matrix representing the online window data, Operators that represent data features Data characteristics representing time;

[0031] Traverse the historical feature trajectories of historical spatiotemporal segments in the historical spatiotemporal dynamic library, and calculate the distance similarity between each historical feature trajectory and the current feature trajectory, referring to the following formula:

[0032]

[0033] in, Indicates the first The distance between a historical spatiotemporal segment and the current feature trajectory of the online window data. Indicates the first Feature trajectory matrix of a historical spatiotemporal segment Represents the characteristic weighting matrix;

[0034] Based on the distance similarity, multiple candidate historical spatiotemporal segments with low similarity are extracted from the historical spatiotemporal dynamic database. These candidate historical spatiotemporal segments are then mixed with the online window data to generate mixed training samples, as shown in the following formula:

[0035]

[0036] in, This represents the mixed training samples generated within the time window W. Indicates the window time collected during the online phase. The DPS status data matrix inside, Let represent the j-th candidate historical spatiotemporal segment with low similarity, and r represent the number of candidate historical spatiotemporal segments with low similarity.

[0037] The spatiotemporal prediction model is dynamically updated based on the spatiotemporal forgetting factor and the mixed training samples, referring to the following formula:

[0038]

[0039]

[0040] Where Y represents the DPS status data matrix during the offline phase, Indicates the length of the time window. The forgetting factor represents the spatial basis functions. This represents the dynamically updated spatial basis function matrix. This represents the forgetting factor in the time coefficient matrix prediction model. This represents the time coefficient predictor of the original spatiotemporal prediction model. This represents the updated time coefficient predictor.

[0041] Optionally, the offline stage state data of the collected distributed parameter system is collected, and KL decomposition is performed on the offline stage state data to obtain the spatial basis function and time coefficient matrix, including:

[0042] Data is collected from the distributed parameter system in the offline stage by multiple sensors deployed on industrial equipment to obtain offline stage status data, which includes DPS status data at multiple time points.

[0043] The offline stage state data is subjected to discrete KL decomposition to obtain the spatial basis function and time coefficient matrix, as shown in the following formula:

[0044]

[0045]

[0046]

[0047] in, Represents the spatial basis function matrix, The dimension of the basis function matrix is ​​represented. Let k be the spatial basis function. Represents the time coefficient matrix. Let M represent the dimension of the time coefficient matrix, and let a(M) represent the time coefficient matrix at the Mth time point. denoted as KL decomposition operation, N represents the number of spatial sampling points, M represents the number of temporal sampling points, Y represents the DPS state data matrix, and k is the number of spatial basis functions extracted.

[0048] Optionally, constructing a spatiotemporal prediction model based on the spatial basis function and the time coefficient matrix includes:

[0049] A time coefficient predictor based on a neural network predicts the time coefficient matrix and generates time prediction coefficients, as shown in the following formula:

[0050]

[0051] in, Indicates the time prediction coefficient. Indicates a time coefficient predictor. Represents a vector of historical time coefficient matrices. This indicates the number of steps in the historical time coefficient matrix that need to be referenced during prediction. Represents the historical input vector. This indicates the number of historical input steps that need to be referenced during prediction;

[0052] A spatiotemporal prediction model is constructed based on the time prediction coefficients and the spatial basis functions, and the spatiotemporal prediction model refers to the following formula:

[0053]

[0054] in, Indicates the DPS status in spatial location ,time Spatiotemporal prediction values ​​at the location.

[0055] Furthermore, to achieve the above objectives, this invention also proposes an adaptive continuous learning spatiotemporal modeling device for time-varying distributed parameter systems. This device is applied to the modeling and analysis of distributed parameter systems in process industries, including chemical, metallurgical, and energy industries. The adaptive continuous learning spatiotemporal modeling device for time-varying distributed parameter systems includes:

[0056] The offline data decomposition module is used to collect offline stage state data of the distributed parameter system and perform KL decomposition on the offline stage state data to obtain spatial basis functions and time coefficient matrices. The offline stage state data is the spatiotemporal state data of the system under stable operating conditions collected by multiple spatial point sensors. The offline stage state data includes time series data of temperature, humidity, concentration, flow rate and / or pressure.

[0057] A spatiotemporal prediction modeling module is used to construct a spatiotemporal prediction model based on the spatial basis function and the time coefficient matrix. The spatiotemporal prediction model includes a time coefficient predictor and a spatial prediction model.

[0058] The online data analysis module is used to collect online phase status data in response to the distributed parameter system being in the online phase. It uses a spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis to perform multi-scale spatiotemporal nonstationarity analysis on the online phase status data. By calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain, it adaptively generates a spatiotemporal forgetting factor that matches the current dynamic rate of change. The online phase status data is the spatiotemporal status data of the system under dynamic operating conditions collected by multiple spatial point sensors. The online phase status data includes time series data of temperature, humidity, concentration, flow rate and / or pressure.

[0059] The model dynamic update module is used to determine the model update weights based on the spatiotemporal forgetting factor, dynamically update the spatiotemporal prediction model based on the model update weights and the coupled generative spatiotemporal replay learning mechanism, and return to execute the steps of collecting online stage state data, using the spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis to perform multi-scale spatiotemporal nonstationarity analysis on the online stage state data, and adaptively generating a spatiotemporal forgetting factor that matches the current dynamic change rate by calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain, until the distribution parameter system ends the online stage. The spatiotemporal replay learning mechanism generates pseudo-samples by querying the degree of matching with historical data, and mixes them with the online stage state data to generate spatiotemporal data, which is used for updating the spatiotemporal prediction model.

[0060] The spatiotemporal prediction and analysis module is used to model and analyze the distributed parameter system based on the dynamically updated spatiotemporal prediction model.

[0061] Furthermore, to achieve the above objectives, this application also proposes an adaptive continuous learning spatiotemporal modeling device for time-varying distributed parameter systems. The device includes: a memory, a processor, and an adaptive continuous learning spatiotemporal modeling program for time-varying distributed parameter systems stored in the memory. The processor is used to run the adaptive continuous learning spatiotemporal modeling program for time-varying distributed parameter systems. The computer program is configured to implement the steps of the adaptive continuous learning spatiotemporal modeling method for time-varying distributed parameter systems as described above.

[0062] In addition, to achieve the above objectives, this application also proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the time-varying distributed parameter system spatiotemporal modeling method for adaptive continuous learning as described above.

[0063] This invention first collects offline DPS data of a distributed parameter system during the offline phase, performs KL decomposition to obtain spatial basis functions and temporal coefficients, and constructs an initial spatiotemporal prediction model containing a temporal coefficient predictor and spatial basis functions. In response to the distributed parameter system entering the online operation phase, this invention executes the following iterative steps: collecting online DPS data and quantifying the spatiotemporal nonstationarity of the system in real time; adaptively generating a spatiotemporal forgetting factor using a multi-criteria inference mechanism to dynamically match the model's update rhythm with the time-varying rhythm of the system's dynamics; simultaneously, combining a spatiotemporal collaborative replay learning mechanism to construct a hybrid augmented training set through recalling and consolidating historical core spatiotemporal dynamic modes; and dynamically updating the spatiotemporal prediction model based on the spatiotemporal forgetting factor and the hybrid augmented training set until the online phase ends. Through the above technical solution, this invention utilizes the dual drive of adaptive forgetting factor and historical replay to achieve accurate tracking of time-varying spatiotemporal dynamics while effectively overcoming the catastrophic forgetting challenge during continuous learning, significantly improving the model's prediction accuracy and robustness for distributed parameter systems in complex nonstationary environments. Attached Figure Description

[0064] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0065] Figure 1 This is a schematic diagram of the spatiotemporal modeling device for an adaptive and continuous learning time-varying distributed parameter system of the hardware operating environment involved in the embodiments of the present invention;

[0066] Figure 2 This is a flowchart illustrating an embodiment of the time-varying distributed parameter system spatiotemporal modeling method of adaptive continuous learning according to the present invention;

[0067] Figure 3 A schematic diagram of the spatiotemporal modeling process for a time-varying distributed parameter system for adaptive continuous learning;

[0068] Figure 4 A schematic diagram of the spatiotemporal modeling technology framework for time-varying distributed parameter systems for adaptive continuous learning;

[0069] Figure 5 This is a structural block diagram of an embodiment of the time-varying distributed parameter system spatiotemporal modeling device for adaptive continuous learning according to the present invention.

[0070] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0071] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0072] Reference Figure 1 , Figure 1 This is a schematic diagram of the spatiotemporal modeling device for an adaptive continuous learning time-varying distributed parameter system for the hardware operating environment involved in the embodiments of the present invention.

[0073] like Figure 1 As shown, the spatiotemporal modeling device for the adaptive continuous learning time-varying distributed parameter system may include: a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. The communication bus 1002 is used to enable communication between these components. The user interface 1003 may include a display screen or an input unit such as a keyboard; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wireless-Fidelity (Wi-Fi) interface). The memory 1005 may be high-speed random access memory (RAM) or stable non-volatile memory (NVM), such as a disk drive. The memory 1005 may also optionally be a storage device independent of the aforementioned processor 1001.

[0074] Those skilled in the art will understand that Figure 1 The structure shown does not constitute a limitation on the spatiotemporal modeling apparatus for time-varying distributed parameter systems of adaptive continuous learning, and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0075] like Figure 1 As shown, the memory 1005, which is a computer-readable storage medium, may include an operating system, a network communication module, a user interface module, and an adaptive continuous learning spatiotemporal modeling program for time-varying distributed parameter systems.

[0076] exist Figure 1In the adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling device shown, the network interface 1004 is mainly used for data communication with the network server; the user interface 1003 is mainly used for data interaction with the user; the processor 1001 and memory 1005 in the adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling device of the present invention can be set in the adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling device. The adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling device calls the adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling program stored in the memory 1005 through the processor 1001, and executes the adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling method provided in the embodiment of the present invention.

[0077] This invention provides an adaptive, continuous learning-based spatiotemporal modeling method for time-varying distributed parameter systems, referring to... Figure 2 , Figure 2 This is a flowchart illustrating an embodiment of the time-varying distributed parameter system spatiotemporal modeling method of the present invention, which is based on adaptive continuous learning.

[0078] In this embodiment, the method is applied to the modeling and analysis of distributed parameter systems in process industries, including chemical, metallurgical, and energy industries. The adaptive continuous learning spatiotemporal modeling method for time-varying distributed parameter systems includes the following steps:

[0079] Step S10: Collect offline stage state data of the distributed parameter system, and perform KL decomposition on the offline stage state data to obtain the spatial basis function and time coefficient matrix.

[0080] It should be noted that this embodiment is applied to the modeling and analysis of distributed parameter systems in process industries. For the spatiotemporal modeling task of distributed parameter systems in complex industrial processes, considering the challenge of decreased prediction accuracy caused by the spatiotemporal dynamic changes due to the time-varying system parameters, this embodiment performs spatiotemporal modeling in the offline stage to generate an initial spatiotemporal prediction model. Then, by collecting data and performing spatiotemporal nonstationarity analysis in the online stage, and replaying and learning from historical spatiotemporal dynamics, the catastrophic forgetting challenge in the continuous learning process is overcome, and the spatiotemporal prediction model is adaptively updated to ensure that the model is consistent with the real spatiotemporal dynamics of the distributed parameter system, thereby improving the spatiotemporal prediction accuracy.

[0081] It should be understood that the executing entity of this embodiment can be a computing service device with data processing, network communication, and program execution functions, such as a tablet computer, personal computer, or mobile phone, or a terminal electronic device capable of performing the above functions. The following description uses an adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling device (hereinafter referred to as the modeling device) as an example to illustrate this embodiment and the following embodiments.

[0082] It should be noted that the offline phase state data can be spatiotemporal multidimensional data about the system state (such as temperature and concentration) collected by the distributed parameter system during the offline phase (the initial preparation phase for stable operation, used for initial modeling), and is a multivariate function of time and space. The offline phase state data is spatiotemporal state data under stable operating conditions collected by multiple spatially located sensors, and includes time-series data of temperature, humidity, concentration, flow rate, and / or pressure.

[0083] Taking the DPS modeling of a chemical reactor as an example, offline status data can include: temperature data collected every 5 minutes for 72 consecutive hours by 20 temperature sensors arranged axially (top, middle, bottom) and radially (center, inner wall) inside the reactor, under rated capacity, fixed feed composition (e.g., methanol-ethanol mixture, ratio 3:1), and stable stirring rate (30 r / min); pressure data collected every 10 minutes by pressure sensors at the reactor inlet and outlet; and reactant and product concentration data obtained from sampling and analysis at different locations inside the reactor (sampling every 30 minutes). Similarly, for the DPS modeling of a metallurgical sintering machine, offline data can include temperature, permeability, and material layer thickness data for different areas (head, middle, tail) of the sintering machine trolley, as well as sulfur dioxide concentration data in the flue gas.

[0084] It should be noted that Distributed Parameter Systems (DPS) are dynamic systems whose core feature is that state variables need to be described by both time and spatial location. Their state evolution cannot be characterized by a single or a small number of centralized parameters, and the heterogeneity of spatial distribution must be considered.

[0085] For example, in the chemical industry, this includes: reaction vessels (internal temperature and concentration distribution varying with time and axial / radial position), distillation columns (temperature and component concentration spatiotemporal distribution across different trays), fixed-bed reactors (temperature and conversion rate distribution of the catalyst bed), and heat exchangers (temperature of the medium within heat exchange tubes varying along tube length and time). In the metallurgical industry, this includes: sintering machines (temperature and permeability spatiotemporal distribution of the material bed on the sintering machine), blast furnaces (temperature and gas composition varying along furnace height and time), and converters (temperature and composition of the molten pool varying with position and smelting time). In the power energy sector, this may include: power plant boilers (temperature and flue gas composition spatiotemporal distribution within the furnace), and steam turbine condensers (temperature distribution of the heat exchange surface varying with time and position).

[0086] Understandably, KL decomposition (Karhunen-Loève decomposition) is used to decompose spatiotemporal data or stochastic processes into a linear combination of orthogonal basis functions. Here, it is approximated by singular value decomposition and used to extract basis functions that characterize spatial distribution and coefficients that characterize temporal dynamics.

[0087] It should be understood that this embodiment decomposes the offline stage state data using KL decomposition, thereby decoupling the high-dimensional, spatiotemporally coupled offline data into spatial and temporal components, reducing modeling complexity, and providing a structured spatiotemporal representation for subsequent model construction.

[0088] In some embodiments, the modeling device collects spatiotemporal state data (such as temperature distribution data with spatial location and time) through multiple spatial point sensors (such as thermocouples and concentration sensors at different locations) during the offline stage of distributed parameter systems in process industries (such as heaters in oil refineries and distillation columns in chemical plants). Using KL decomposition, the offline stage state data matrix is ​​decomposed into a spatial basis function matrix (describing the spatial distribution pattern of the system state) and a time coefficient matrix (describing the weight changes of the spatial basis functions in the time dimension).

[0089] It is understandable that the DPS in the actual process can be described using parabolic PDEs as shown in Formula 1:

[0090] , formula 1

[0091] The boundary conditions and initial conditions are shown in Equations 2 and 3, respectively:

[0092] , formula 2

[0093] , formula 3

[0094] in, For time variables, For spatial variables, Indicates that the system is in Moment The state value at the location, for System control input at any given time, The representative contains Nonlinear functions of the spatial differential operator of order, This represents the function by which the control input affects the system. Represents a nonlinear function. and These represent the variable parameters related to the system state and control input, respectively. These parabolic PDEs can be used to describe real-world industrial phenomena such as temperature distribution processes and reaction-diffusion processes.

[0095] To achieve the spatiotemporal prediction task of distributed parameter systems, a model needs to be established to realize the process shown in Equation 4 below:

[0096] , formula 4

[0097] in, This represents the spatiotemporal prediction model that needs to be established. and These represent the lag lengths of the system state input and control input, respectively. Considering the time-varying phenomena of system parameters during system operation, an algorithm needs to be designed to update the spatiotemporal prediction model online to ensure that the model tracks and learns the spatiotemporal dynamics of DPS and makes accurate predictions.

[0098] Furthermore, to improve the spatiotemporal learning effect and increase the modeling accuracy, the above step S10 in the offline stage may include:

[0099] Step S101: Collect data from the distributed parameter system in the offline stage using multiple sensors deployed on industrial equipment to obtain offline stage status data, which includes DPS status data at multiple time points.

[0100] Step S102: Perform discrete KL decomposition on the offline stage state data to obtain the spatial basis function and time coefficient matrix.

[0101] Understandably, during the offline phase, assuming deployment on industrial equipment... Each sensor collects information (e.g., placed on a volatilization kiln or heating furnace). (Each thermocouple measures the temperature at different locations, and continuous sampling is used to obtain...) The DPS status data at each time point is denoted as: According to the discrete KL decomposition, DPS data can be approximated using singular value decomposition to obtain the corresponding nth-order principal spatial basis functions and the corresponding time coefficient matrix, as shown in Equations 5.1, 5.2, and 5.3 below:

[0102] , Formula 5.1

[0103] , Formula 5.2

[0104] , Formula 5.3

[0105] in, Represents the spatial basis function matrix, The dimension of the basis function matrix is ​​represented. Let k be the spatial basis function. Represents the time coefficient matrix. Let M represent the dimension of the time coefficient matrix, and let a(M) represent the time coefficient matrix at the Mth time point. denoted as KL decomposition operation, N represents the number of spatial sampling points, M represents the number of temporal sampling points, Y represents the DPS state data matrix, and k is the number of spatial basis functions extracted.

[0106] Step S20: Construct a spatiotemporal prediction model based on the spatial basis function and the time coefficient matrix.

[0107] It should be noted that the spatiotemporal prediction model includes a time coefficient predictor and a spatial prediction model. The spatiotemporal prediction model consists of a time coefficient predictor (handling dynamics in the time dimension) and a spatial basis function (handling spatial distribution), and is used to predict the state of the distributed parameter system in the spatiotemporal domain.

[0108] In some embodiments, spatial basis functions are directly used to characterize the spatial distribution pattern of the system state; the time coefficient matrix prediction model adopts a neural network model (such as Long Short-Term Memory Network LSTM, Gated Recurrent Unit GRU), takes the historical time coefficient matrix and system input (such as valve opening degree, heating power) as input, learns the dynamic evolution law of the time coefficient matrix, and realizes the prediction of the time coefficient matrix.

[0109] Furthermore, in order to improve the predictive ability of the spatiotemporal state of the distributed parameter system, step S20 above may include:

[0110] Step S201: The time coefficient matrix is ​​predicted based on a neural network-based time coefficient predictor to generate time prediction coefficients;

[0111] Step S202: Construct a spatiotemporal prediction model based on the time prediction coefficients and the spatial basis functions.

[0112] It is understandable that a neural network-based time coefficient predictor would be designed for the time coefficient matrix. To achieve the time coefficient matrix prediction process as shown in Formula 6:

[0113] , formula 6

[0114] in, Indicates the time prediction coefficient. Indicates a time coefficient predictor. Represents a vector of historical time coefficient matrices. This indicates the number of steps in the historical time coefficient matrix that need to be referenced during prediction. Represents the historical input vector. This indicates the number of steps of historical input that need to be referenced during prediction.

[0115] Based on the predicted time coefficient matrix and the existing spatial basis functions, spatiotemporal synthesis is performed to obtain the spatiotemporal prediction result of the DPS state, as shown in Formula 7:

[0116] , Formula 7

[0117] in, Indicates the DPS status in spatial location ,time The spatiotemporal prediction values ​​at the location. Thus, based on the offline collected DPS spatiotemporal data, an initial spatiotemporal prediction model has been established.

[0118] Step S30: In response to the distributed parameter system being in the online stage, collect the online stage state data, use the spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis to perform multi-scale spatiotemporal nonstationarity analysis on the online stage state data, and adaptively generate a spatiotemporal forgetting factor that matches the current dynamic change rate by calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain.

[0119] It should be noted that the online stage status data is the spatiotemporal status data of the system under dynamic operating conditions collected by multiple spatial point sensors. The online stage status data includes time series data of temperature, humidity, concentration, flow rate and / or pressure.

[0120] It should be noted that the online phase state data mentioned in this embodiment refers to the spatiotemporal state data characterizing the dynamic physical field properties of the distributed parameter system, collected by pre-deployed multi-point sensors during the online operation phase (real-time operation phase). This data aims to provide real-time information flow for parameter correction of the spatiotemporal prediction model, and its physical types include, but are not limited to, time-series data of physical quantities such as temperature, humidity, concentration, flow rate, and pressure. The spatiotemporal forgetting factor is an adaptive parameter used to dynamically adjust the weighting ratio of historical memory data to current new data during online incremental learning. This factor aims to track the non-stationary time-varying characteristics of the system by controlling the decay rate of historical information. Specifically, structurally, it is decoupled into: a time coefficient prediction model forgetting factor for updating the time dynamics model, and a spatial basis function forgetting factor for updating spatial structural features.

[0121] Taking a chemical reactor as an example, online status data can include: real-time temperature data collected every minute by 20 temperature sensors used in the offline stage (covering scenarios such as fluctuations in feed composition and fine-tuning of heating power); real-time pressure data collected every 2 minutes by inlet and outlet pressure sensors (which may include external interference information such as pipeline pressure fluctuations); and real-time concentration data of key components inside the reactor fed back by an online concentration detector (updated every 5 minutes). Similarly, in DPS modeling of a heat exchanger, online data can include real-time temperature at different locations on the heat exchange tubes, inlet and outlet medium flow rates, medium viscosity, and dynamic changes in ambient temperature (external interference factors).

[0122] It should be noted that when a distributed parameter system is online, its spatiotemporal dynamics often exhibit complex non-stationary characteristics due to the time-varying nature of parameters in the actual operating environment. Traditional static models or methods based on fixed update strategies struggle to effectively perceive and adapt to such dynamic changes, leading to a decline in prediction performance. Therefore, this embodiment aims to provide an adaptive online learning mechanism that endows the prediction model with real-time perception and adaptive adjustment capabilities regarding the degree of spatiotemporal dynamic evolution of the system. Its core logic is as follows: when a significant change in the system's spatiotemporal dynamics is detected, the mechanism adaptively increases the model update rate, prompting the model to quickly forget outdated information and capture the latest spatiotemporal dynamic characteristics; when the system is in a quasi-steady state or undergoing slow changes, the mechanism suppresses excessive parameter updates, thereby consolidating existing historical knowledge and preventing parameter oscillations caused by noise interference.

[0123] Furthermore, in order to accurately perceive the time-varying characteristics of the distributed parameter system and improve the spatiotemporal response capability of the model, in one embodiment, the spatiotemporal forgetting factor includes a temporal forgetting factor and a spatial forgetting factor, and the above step S30 may include:

[0124] Step S301: In response to the distributed parameter system being in the online stage, collect online stage status data, which includes DPS status data within multiple time windows in the online state;

[0125] Step S302: Perform spatiotemporal nonstationarity analysis on the online stage state data to obtain spatiotemporal nonstationarity indices of the DPS state data within the time window. The spatiotemporal nonstationarity indices include spatial projection reconstruction error and time prediction residual. The spatiotemporal nonstationarity analysis process includes: calculating the spatial projection reconstruction error on the subspace formed by the online stage state data and the spatial basis function to quantify the degree of structural variation of the system's spatial distribution mode; and calculating the time prediction residual of the prediction model of the time coefficient matrix for the time coefficient at the current moment to quantify the degree of dynamic variation of the system's time evolution law.

[0126] Step S303: Construct a fuzzy mapping based on spatiotemporal nonstationary indices to divide the numerical range of the spatial projection reconstruction error and the time prediction residual into multiple fuzzy subsets covering different intervals;

[0127] Step S304: Input the values ​​of the spatial projection reconstruction error and the time prediction residual obtained in the online stage into the preset membership function respectively, and calculate the membership values ​​of the values ​​belonging to each fuzzy subset, so as to convert the rigid scalar into two independent spatiotemporal fuzzy membership vectors.

[0128] Step S305: Input the spatiotemporal fuzzy membership vector into the fuzzy inference engine, activate the corresponding spatial adjustment rules and temporal adjustment rules respectively, and infer the temporal forgetting factor and spatial forgetting factor.

[0129] In some embodiments, during the online phase, sensors collect online phase status data in real time within a window period to calculate spatiotemporal nonstationary indices (such as spatial projection error SVC, time variation coefficient TVC, and overall prediction error OVC). Fuzzy inference techniques are introduced to fuzzify these indices (defining fuzzy linguistic variables such as "low, medium, and high" and calculating membership degrees using triangular membership functions, etc.), perform fuzzy rule inference (such as the rule "if SVC is high and TVC is high, then the forgetting factor is large"), and defuzzify (such as the centroid method) to generate spatiotemporal forgetting factors (including time coefficient matrix model forgetting factors and spatial basis function forgetting factors).

[0130] Furthermore, to accurately calculate the degree of spatiotemporal nonstationarity within a time window, in one embodiment, the spatiotemporal nonstationarity index includes spatial projection reconstruction error and time prediction residual; the process of spatiotemporal nonstationarity analysis includes:

[0131] The spatial projection reconstruction error on the subspace formed by the online phase state data and the spatial basis function is calculated to quantify the degree of structural variation of the system's spatial distribution modes.

[0132] The prediction model of the time coefficient matrix is ​​calculated to obtain the time prediction residual of the time coefficient at the current moment, so as to quantify the degree of dynamic variation of the system's time evolution law.

[0133] In the specific implementation, the modeling device collects DPS data online within a window period, denoted as: ,in, Indicates the window length. According to... To calculate the degree of spatiotemporal nonstationarity within this time window, refer to the following formulas 8 and 9:

[0134] , formula 8

[0135] , formula 9

[0136] Where SVC represents spatial projection reconstruction error. Formula 8 evaluates the ability of the current preset spatial basis function to capture the main spatial patterns of the data by calculating the spatial projection error of the data within the window. The larger the error value, the worse the representativeness of the basis function to the current spatial structure.

[0137] TVC represents the time prediction residual. Formula 9 quantifies the degree of temporal variation of the window data, and its calculation result directly characterizes the fluctuation level of the system's dynamic characteristics in the current time period.

[0138] W represents the length of the time window, M represents the number of time sampling points, and N represents the number of spatial sampling points. This represents the first step after reconstruction using existing spatial basis functions. The value at each spatial location Indicates the first The values ​​of the original DPS state data at each spatial location. This represents the original time coefficient matrix. Represents the time coefficient matrix for prediction. Indicates spatial location ,time The original DPS state value at that location, Indicates spatial location ,time The predicted DPS state value at the location.

[0139] Furthermore, to obtain the spatiotemporal forgetting factor from spatiotemporal non-stationary characteristic indicators through mapping, a fuzzy logic strategy is introduced for reasoning in one implementation case. First, fuzzy linguistic variables are defined for the spatiotemporal non-stationary indicators, and fuzzy membership functions are introduced to fuzzify the indicators and determine the membership degrees of various indicators. The fuzzy membership functions are typical functions such as trigonometric membership functions and Gaussian membership functions, and the parameters of the functions are calculated from offline historical data. For example, for the time variation coefficient (TVC) in the spatiotemporal non-stationary indicator, three fuzzy linguistic variables are defined: Low, Medium, and High. The membership degrees of the indicators are calculated using trigonometric functions, referring to the following formula 10. The membership functions include:

[0140] , formula 10

[0141] in, , and These represent the membership levels of the time variation coefficient to low, medium, and high values, respectively. This refers to the fuzzy membership function of a triangle. , , , , , , , and These are the parameters of the fuzzy membership function.

[0142] Then, based on the fuzzy rule base and defuzzification, the mapping calculation from spatiotemporal nonstationary indicators to spatiotemporal forgetting factors is realized, as shown in Formula 11 below:

[0143] , formula 11

[0144] in, and These represent the forgetting factors of the time coefficient matrix model and the spatial basis function, respectively. This represents the fuzzy inference process. Through the above mechanism, the prediction model successfully established an adaptive adjustment loop for the forgetting factor driven by the spatiotemporal nonstationarity of DPS online data. This capability effectively overcomes the inherent limitations of traditional fixed update strategies, enabling the model to evolve from a single static prediction tool into an adaptive intelligent entity with environmental awareness; it can not only capture in real time, but also actively respond to and accurately follow the complex spatiotemporal dynamics of DPS evolution.

[0145] Step S40: Determine model update weights based on the spatiotemporal forgetting factor, dynamically update the spatiotemporal prediction model based on the model update weights and the coupled generative spatiotemporal replay learning mechanism, and return to execute the steps of collecting online stage state data, using the spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis to perform multi-scale spatiotemporal nonstationarity analysis on the online stage state data, and adaptively generating a spatiotemporal forgetting factor that matches the current dynamic rate of change by calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain, until the distribution parameter system ends the online stage. The spatiotemporal replay learning mechanism generates pseudo-samples by querying the degree of matching with historical data, and mixes them with the online stage state data to generate spatiotemporal data, which is used for updating the spatiotemporal prediction model.

[0146] It is important to note that during online learning, the spatiotemporal prediction model is continuously updated to learn the latest DPS spatiotemporal dynamics. This exposes it to the risk of catastrophic forgetting, meaning that when adapting to new data, the model rapidly loses its memory of previously learned, but equally important, spatiotemporal dynamic patterns. To overcome this challenge, this example further proposes a generative spatiotemporal replay learning mechanism to construct hybrid augmented training samples that incorporate current real-time perception information and historical key dynamic modes. This mechanism achieves synergistic optimization of old and new spatiotemporal modes by forcibly introducing review signals from historical experience during the online model update process. This ensures that the model can readily adapt to new conditions while effectively retaining its long-term memory of historical conditions, preventing excessive drift of model parameters in non-stationary environments.

[0147] Furthermore, to improve the model's prediction accuracy, step S40 above may include:

[0148] Step S401: Construct a historical spatiotemporal dynamic library based on the DPS status data matrix from the offline phase;

[0149] Step S402: Analyze the current feature trajectory of the online window data time by time. The current feature trajectory is composed of data features of multiple times within the window time. The online window data is the DPS status data matrix collected during the window time in the online phase.

[0150] Step S403: Traverse the historical feature trajectories of historical spatiotemporal segments in the historical spatiotemporal dynamic library, and calculate the distance similarity between each historical feature trajectory and the current feature trajectory;

[0151] Step S404: Based on the distance similarity, extract multiple candidate historical spatiotemporal segments with low similarity from the historical spatiotemporal dynamic library, and mix the candidate historical spatiotemporal segments with the online window data to generate mixed training samples;

[0152] Step S405: Determine the model update weights based on the spatiotemporal forgetting factor, and dynamically update the spatiotemporal prediction model based on the update weights and the mixed training samples, combined with the spatiotemporal replay learning mechanism.

[0153] It should be noted that, firstly, during the offline phase, a historical spatiotemporal dynamic library is established: This historical spatiotemporal dynamics library is designed to store the historical spatiotemporal dynamics of the DPS operation process, providing "memory samples" as a data foundation for subsequent model updates.

[0154] To track system dynamics across both time and space dimensions, the spatial basis functions and the time coefficient matrix model should be updated separately. (Based on online window data...) The Mahalanobis distance similarity method is used to extract similar working condition data that are highly physically correlated with the current system operation mode from historical data. First, the time-by-time statistical feature trajectory of the online data is calculated, referring to the following formula 12:

[0155] , formula 12

[0156] in, This represents online window data. The feature trajectory matrix representing the online window data, Operators that represent data features Data characteristics representing time;

[0157] Then, iterate through the spatiotemporal segment feature trajectories of the historical dynamic library. Calculate the distance similarity between it and the current feature trajectory. Refer to Formula 13 below:

[0158] , Formula 13

[0159] in, Indicates the first The distance between a historical spatiotemporal segment and the current feature trajectory of the online window data. Indicates the first Feature trajectory matrix of a historical spatiotemporal segment Represents the characteristic weighting matrix;

[0160] Select the r historical spatiotemporal data segments with the lowest similarity This data is then mixed with online window data to generate training samples, as shown in Formula 14 below:

[0161] , Formula 14

[0162] in, This represents the mixed training samples generated within the time window W. Indicates the window time collected during the online phase. The DPS status data matrix inside, Let represent the j-th candidate historical spatiotemporal segment with low similarity, and r represent the number of candidate historical spatiotemporal segments with low similarity.

[0163] Finally, an online collaborative update step for the spatiotemporal prediction model is performed. Specifically, an adaptive spatiotemporal forgetting factor generated based on nonstationarity analysis and hybrid replay training samples constructed based on a generative mechanism are used to iteratively correct the model's spatial basis functions and temporal coefficient prediction model (dynamic parameters), respectively. The specific mathematical update process is illustrated in Equations 15 and 16 below. Through this collaborative update strategy, this invention achieves accurate tracking of the dynamic characteristics of time-varying distributed parameter systems, ensuring both model plasticity and stability, thereby significantly ensuring the accuracy of online spatiotemporal prediction.

[0164] , formula 15

[0165] , Formula 16

[0166] Where Y represents the DPS status data matrix during the offline phase, This represents the generated mixed training samples. The forgetting factor represents the spatial basis functions. Represents the dynamically updated spatial basis function matrix This represents the forgetting factor in the time coefficient matrix prediction model. This represents the time coefficient predictor of the original spatiotemporal prediction model. This represents the updated time coefficient predictor.

[0167] Step S50: Model and analyze the distributed parameter system based on the dynamically updated spatiotemporal prediction model.

[0168] In its implementation, the modeling device first initializes the model based on offline DPS data, including the extraction of spatial basis functions and the establishment of a temporal coefficient prediction model. Upon entering the online phase, the device continuously captures streaming data containing new spatiotemporal dynamics and analyzes its spatiotemporal non-stationary characteristics in real time. Based on this, on the one hand, it uses fuzzy inference technology to adaptively generate a spatiotemporal forgetting factor, achieving sensitive tracking of non-stationary changes; on the other hand, it calls upon memory information from the historical spatiotemporal dynamics library to perform replay learning, suppressing catastrophic forgetting through mixed training of new and old knowledge. After completing the adaptive update of the model, the device orthogonally synthesizes the predicted output of the temporal coefficient model with the real-time updated spatial basis functions, thereby achieving accurate prediction of the future spatiotemporal state of the distributed parameter system.

[0169] The modeling method flowchart and overall framework diagram of this embodiment are as follows: Figure 3 and Figure 4 As shown, Figure 3 This is a schematic diagram of the spatiotemporal modeling process for a time-varying distributed parameter system with adaptive continuous learning. Figure 4A schematic diagram of the spatiotemporal modeling technology framework for time-varying distributed parameter systems for adaptive continuous learning.

[0170] Understandably, the core value of this embodiment lies in providing a general adaptive spatiotemporal modeling paradigm that can effectively address the challenges of predicting time-varying distributed parameter systems prevalent in process industries. Based on spatiotemporal separation, this method innovatively combines a non-stationarity-driven adaptive adjustment mechanism for the forgetting factor with a replay-based memory retention mechanism. This dual-driven strategy not only ensures the model's rapid tracking of current operating conditions but also guarantees long-term retention of historical experience. Therefore, this method has extremely high industrial application potential and can be deployed in various real-world production scenarios with spatiotemporal coupling characteristics, including but not limited to monitoring the temperature field of zinc oxide volatilization kilns, predicting concentration distribution in chemical reactors, or controlling the temperature of hot-rolled steel.

[0171] In practical implementation, the modeling device can input the latest collected online stage status data into the dynamically updated spatiotemporal prediction model, and output the time coefficient matrix of the future preset time period (such as the next 10 minutes or 30 minutes) through the model's time coefficient matrix prediction module. Combined with the corrected spatial basis function, the spatiotemporal state is reconstructed to obtain the future spatiotemporal distribution prediction results of the system (such as the predicted values ​​of temperature and concentration at different spatial locations).

[0172] In some embodiments, modeling and analysis can be implemented to conduct targeted modeling and analysis based on the actual needs of the process industry:

[0173] State prediction analysis: By comparing the spatiotemporal state predicted by the model with the actual operating threshold of the system, it is possible to predict whether the system will experience abnormal states (such as excessive temperature or concentration deviating from the set value).

[0174] Fault diagnosis and analysis: If the predicted results deviate significantly from the actual monitored values, analyze the source of the deviation by combining the historical fault sample library, and determine whether there are problems such as sensor failure or abnormal equipment operation.

[0175] Parameter optimization analysis: Based on the predicted spatiotemporal state distribution, the optimal operating parameters (such as feed flow rate and heating power) are derived in reverse to provide decision support for production optimization; the analysis results are output to the industrial monitoring platform in a visual form (such as spatiotemporal distribution heat map and trend curve).

[0176] This embodiment first utilizes the KL decomposition characteristics of offline data to construct a spatiotemporally decoupled initial prediction architecture. During the online operation phase, this scheme innovatively introduces a non-stationarity-driven adaptive model update loop: by real-time monitoring of the non-stationarity index of online data, a spatiotemporal forgetting factor is dynamically generated, and in conjunction with generative spatiotemporal experience replay technology, the model is incrementally corrected online. This process constitutes a continuously learning dynamic closed loop, constantly iterating the model update prediction steps until the system shuts down. This mechanism solves the catastrophic forgetting problem of traditional models under non-stationary spatiotemporal dynamics. By adaptively adjusting the model's plasticity (adapting to new data) and stability (preserving old memories), this embodiment significantly improves the model's ability to track complex time-varying dynamics and its predictive robustness.

[0177] Furthermore, this embodiment of the invention also proposes a computer-readable storage medium storing an adaptive continuous learning spatiotemporal modeling program for a time-varying distributed parameter system. When the adaptive continuous learning spatiotemporal modeling program for a time-varying distributed parameter system is executed by a processor, it implements the steps of the adaptive continuous learning spatiotemporal modeling method for a time-varying distributed parameter system as described above.

[0178] The computer-readable storage medium provided in this application may be, for example, a USB flash drive, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, system, or device. The program code contained on the computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination thereof.

[0179] The aforementioned computer-readable storage medium may be included in the spatiotemporal modeling device of the adaptive continuous learning time-varying distributed parameter system; or it may exist independently and not be assembled into the spatiotemporal modeling device of the adaptive continuous learning time-varying distributed parameter system.

[0180] Furthermore, this invention also proposes a computer program product, including an adaptive continuous learning spatiotemporal modeling program for time-varying distributed parameter systems. When the adaptive continuous learning spatiotemporal modeling program for time-varying distributed parameter systems is executed by a processor, it implements the steps of the adaptive continuous learning spatiotemporal modeling method for time-varying distributed parameter systems as described above.

[0181] The specific implementation of the computer program product of the present invention is basically the same as the various embodiments of the above-described adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling method, and will not be repeated here.

[0182] Reference Figure 5 , Figure 5 This is a structural block diagram of an embodiment of the time-varying distributed parameter system spatiotemporal modeling device for adaptive continuous learning according to the present invention.

[0183] like Figure 5 As shown in the embodiment of the present invention, an adaptive continuous learning spatiotemporal modeling device for time-varying distributed parameter systems is proposed. This device is applied to the modeling and analysis of distributed parameter systems in process industries, including chemical, metallurgical, and energy industries. The device includes:

[0184] The offline data decomposition module 10 is used to collect offline stage state data of the distributed parameter system and perform KL decomposition on the offline stage state data to obtain spatial basis functions and time coefficient matrices. The offline stage state data is the spatiotemporal state data of the system under stable operating conditions collected by multiple spatial point sensors. The offline stage state data includes time series data of temperature, humidity, concentration, flow rate and / or pressure.

[0185] Spatiotemporal prediction modeling module 20 is used to construct a spatiotemporal prediction model based on the spatial basis function and the time coefficient matrix. The spatiotemporal prediction model includes a time coefficient predictor and a spatial prediction model.

[0186] The online data analysis module 30 is used to collect online stage status data in response to the distributed parameter system being in the online stage. It uses a spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis to perform multi-scale spatiotemporal nonstationarity analysis on the online stage status data. It also adaptively generates a spatiotemporal forgetting factor that matches the current dynamic change rate by calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain. The online stage status data is the spatiotemporal status data of the system under dynamic operating conditions collected by multiple spatial point sensors. The online stage status data includes time series data of temperature, humidity, concentration, flow rate and / or pressure.

[0187] The model dynamic update module 40 is used to determine the model update weights based on the spatiotemporal forgetting factor, dynamically update the spatiotemporal prediction model based on the model update weights and the coupled generative spatiotemporal replay learning mechanism, and return to execute the steps of collecting online stage state data, using the spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis to perform multi-scale spatiotemporal nonstationarity analysis on the online stage state data, and adaptively generating a spatiotemporal forgetting factor that matches the current dynamic change rate by calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain, until the distribution parameter system ends the online stage. The spatiotemporal replay learning mechanism generates pseudo-samples by querying the degree of matching with historical data, and mixes them with the online stage state data to generate spatiotemporal data, which is used for updating the spatiotemporal prediction model.

[0188] The spatiotemporal prediction and analysis module 50 is used to model and analyze the distributed parameter system based on the dynamically updated spatiotemporal prediction model.

[0189] This embodiment first collects offline DPS data of the distributed parameter system during the offline phase, performs KL decomposition to obtain spatial basis functions and temporal coefficients, and constructs an initial spatiotemporal prediction model containing a temporal coefficient predictor and spatial basis functions. In response to the distributed parameter system entering the online operation phase, this invention executes the following iterative steps: collecting online DPS data and quantifying the spatiotemporal nonstationarity of the system in real time; adaptively generating a spatiotemporal forgetting factor using a multi-criteria inference mechanism to dynamically match the model's update rhythm with the variable-scale time-varying rhythm of the system dynamics; simultaneously, combining a spatiotemporal collaborative replay learning mechanism to construct a hybrid augmented training set through recalling and consolidating historical core spatiotemporal dynamic modes; and dynamically updating the spatiotemporal prediction model based on the spatiotemporal forgetting factor and the hybrid augmented training set until the online phase ends. Through the above technical solution, this invention utilizes the dual drive of adaptive forgetting factor and historical replay to achieve accurate tracking of time-varying spatiotemporal dynamics while effectively overcoming the catastrophic forgetting challenge in the continuous learning process, significantly improving the model's prediction accuracy and robustness for distributed parameter systems in complex nonstationary environments.

[0190] The adaptive continuous learning spatiotemporal modeling device for time-varying distributed parameter systems provided in this application employs the adaptive continuous learning spatiotemporal modeling method for time-varying distributed parameter systems in the above embodiments, and can solve the technical problem of spatiotemporal modeling of adaptive continuous learning time-varying distributed parameter systems. Compared with the prior art, the beneficial effects of the adaptive continuous learning spatiotemporal modeling device for time-varying distributed parameter systems provided in this application are the same as the beneficial effects of the adaptive continuous learning spatiotemporal modeling method for time-varying distributed parameter systems provided in the above embodiments, and other technical features in the adaptive continuous learning spatiotemporal modeling device for time-varying distributed parameter systems are the same as the features disclosed in the methods of the above embodiments, and will not be repeated here.

[0191] It should be understood that the above are merely illustrative examples and do not constitute any limitation on the technical solutions of the present invention. In specific applications, those skilled in the art can make settings as needed, and the present invention does not impose any restrictions on this.

[0192] It should be noted that the workflow described above is merely illustrative and does not limit the scope of protection of this invention. In practical applications, those skilled in the art can select some or all of the workflow to achieve the purpose of this embodiment according to actual needs, and no restrictions are imposed here.

[0193] In addition, for technical details not described in detail in this embodiment, please refer to the spatiotemporal modeling method for time-varying distributed parameter systems with adaptive continuous learning provided in any embodiment of the present invention, which will not be repeated here.

[0194] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0195] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0196] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory / random access memory, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0197] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A self-adaptive continual learning time-varying distribution parameter system spatiotemporal modeling method, characterized in that, The method is applied to the modeling and analysis of distributed parameter systems in process industries, including chemical, metallurgical, and energy industries. The adaptive continuous learning spatiotemporal modeling method for time-varying distributed parameter systems includes: The system collects offline stage state data of the distributed parameter system and performs KL decomposition on the offline stage state data to obtain spatial basis functions and time coefficient matrices. The offline stage state data is the spatiotemporal state data of the system under stable operating conditions collected by multiple spatial point sensors. The offline stage state data includes time series data of temperature, humidity, concentration, flow rate and / or pressure. A spatiotemporal prediction model is constructed based on the spatial basis function and the time coefficient matrix. The spatiotemporal prediction model includes a time coefficient predictor and a spatial prediction model. In response to the distributed parameter system being in the online phase, online phase status data is collected. A spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis is used to perform multi-scale spatiotemporal nonstationarity analysis on the online phase status data. By calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain, a spatiotemporal forgetting factor that matches the current dynamic rate of change is adaptively generated. The online phase status data is the spatiotemporal status data of the system under dynamic operating conditions collected by multiple spatial point sensors. The online phase status data includes time series data of temperature, humidity, concentration, flow rate and / or pressure. The model update weights are determined based on the spatiotemporal forgetting factor. The spatiotemporal prediction model is dynamically updated based on the model update weights and the coupled generative spatiotemporal replay learning mechanism. The process of collecting online stage state data is then performed. The spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis is used to perform multi-scale spatiotemporal nonstationarity analysis on the online stage state data. The steps of adaptively generating a spatiotemporal forgetting factor that matches the current dynamic rate of change by calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain are repeated until the distribution parameter system ends the online stage. The spatiotemporal replay learning mechanism generates pseudo-samples by querying the degree of matching with historical data and mixes them with the online stage state data to generate spatiotemporal data. The spatiotemporal data is used for updating the spatiotemporal prediction model. The distributed parameter system is modeled and analyzed based on the dynamically updated spatiotemporal prediction model. The spatiotemporal forgetting factor includes a temporal forgetting factor and a spatial forgetting factor; in response to the distributed parameter system being in the online stage, online stage state data is collected, and a spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis is used to perform multi-scale spatiotemporal nonstationarity analysis on the online stage state data. Furthermore, by calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain, a spatiotemporal forgetting factor adaptively generates one that matches the current dynamic rate of change, including: In response to the distributed parameter system being in the online phase, online phase status data is collected, which includes DPS status data within multiple time windows under the online state; Spatiotemporal nonstationarity analysis is performed on the online stage state data to obtain spatiotemporal nonstationarity indices of DPS state data within a time window. The spatiotemporal nonstationarity indices include spatial projection reconstruction error and time prediction residual. A fuzzy mapping based on spatiotemporal nonstationary indices is constructed to divide the numerical ranges of the spatial projection reconstruction error and the time prediction residual into multiple fuzzy subsets covering different intervals. The values ​​of spatial projection reconstruction error and time prediction residual obtained from the online stage are input into the preset membership function to calculate the membership values ​​of the values ​​belonging to each fuzzy subset, so as to convert the rigid scalar into two independent spatiotemporal fuzzy membership vectors. The spatiotemporal fuzzy membership vector is input into the fuzzy inference engine, and the corresponding spatial adjustment rules and temporal adjustment rules are activated respectively to infer the temporal forgetting factor and spatial forgetting factor.

2. The self-adapting persistent learning time-varying distribution parameter system space-time modeling method of claim 1, wherein, The process of spatiotemporal nonstationarity analysis includes: The spatial projection reconstruction error on the subspace formed by the online phase state data and the spatial basis function is calculated to quantify the degree of structural variation of the system's spatial distribution modes. The prediction model for the time coefficient matrix is ​​used to calculate the time prediction residual for the time coefficient at the current moment, in order to quantify the degree of dynamic variation in the system's time evolution. The spatial projection reconstruction error and the time prediction residual are calculated using the following formulas: Where SVC represents the spatial projection reconstruction error, TVC represents the temporal prediction residual, W represents the time window length, M represents the number of time sampling points, and N represents the number of spatial sampling points. This represents the first step after reconstruction using existing spatial basis functions. The value at each spatial location Indicates the first The values ​​of the original DPS state data at each spatial location. This represents the original time coefficient matrix. Represents the time coefficient matrix for prediction. Indicates spatial location ,time The original DPS state value at that location, Indicates spatial location ,time The predicted DPS state value at the location.

3. The spatiotemporal modeling method for time-varying distributed parameter systems based on adaptive continuous learning as described in claim 2, characterized in that, The membership function includes: in, , and These represent the membership levels of the time variation coefficient to low, medium, and high values, respectively. It refers to fuzzy membership functions. , , , , , , , and These are the parameters of the fuzzy membership function.

4. The self-adapting persistent learning time-varying distribution parameter system space-time modeling method of claim 3, wherein, The step of determining model update weights based on the spatiotemporal forgetting factor, and dynamically updating the spatiotemporal prediction model based on the model update weights and the coupled generative spatiotemporal replay learning mechanism, includes: A historical spatiotemporal dynamic library is constructed based on the DPS status data matrix during the offline phase; The current feature trajectory is analyzed time-by-time from the online window data, where the online window data is a matrix of DPS state data collected during the window time in the online phase, and the current feature trajectory is composed of data features from multiple moments within the window time: wherein, represents online window data, represents a feature trajectory matrix of the online window data, represents a data feature computation operator, represents a data feature at a time instant; Traverse the historical feature trajectories of historical spatiotemporal segments in the historical spatiotemporal dynamic library, and calculate the distance similarity between each historical feature trajectory and the current feature trajectory, referring to the following formula: in, Indicates the first The distance between a historical spatiotemporal segment and the current feature trajectory of the online window data. Indicates the first Feature trajectory matrix of a historical spatiotemporal segment Represents the characteristic weighting matrix; Based on the distance similarity, multiple candidate historical spatiotemporal segments with low similarity are extracted from the historical spatiotemporal dynamic database. These candidate historical spatiotemporal segments are then mixed with the online window data to generate mixed training samples, as shown in the following formula: in, This represents the mixed training samples generated within the time window W. Indicates the window time collected during the online phase. The DPS status data matrix inside, Let represent the j-th candidate historical spatiotemporal segment with low similarity, and r represent the number of candidate historical spatiotemporal segments with low similarity. Based on the spatiotemporal forgetting factor, the model update weights are determined. Based on the update weights and the mixed training samples, the spatiotemporal prediction model is dynamically updated using a spatiotemporal replay learning mechanism, as shown in the following formula: Where Y represents the DPS status data matrix during the offline phase, Indicates the length of the time window. This represents the generated mixed training samples. The forgetting factor represents the spatial basis functions. This represents the dynamically updated spatial basis function matrix. This represents the forgetting factor in the time coefficient matrix prediction model. This represents the time coefficient predictor of the original spatiotemporal prediction model. This represents the updated time coefficient predictor.

5. The self-adapting persistent learning time-varying distribution parameter system space-time modeling method of any one of claims 1 to 4, wherein, The offline phase state data of the collected distributed parameter system is then subjected to KL decomposition to obtain the spatial basis functions and time coefficient matrix, including: Data is collected from the distributed parameter system in the offline stage by multiple sensors deployed on industrial equipment to obtain offline stage status data, which includes DPS status data at multiple time points. The offline stage state data is subjected to discrete KL decomposition to obtain the spatial basis function and time coefficient matrix, as shown in the following formula: in, Represents the spatial basis function matrix, The dimension of the basis function matrix is ​​represented. Let k be the spatial basis function. Represents the time coefficient matrix. Let M represent the dimension of the time coefficient matrix, and let a(M) represent the time coefficient matrix at the Mth time point. denoted as KL decomposition operation, N represents the number of spatial sampling points, M represents the number of temporal sampling points, Y represents the DPS state data matrix, and k is the number of spatial basis functions extracted.

6. The self-adapting persistent learning time-varying distribution parameter system space-time modeling method of claim 5, wherein, The construction of the spatiotemporal prediction model based on the spatial basis function and the time coefficient matrix includes: A time coefficient predictor based on a neural network predicts the time coefficient matrix and generates time prediction coefficients, as shown in the following formula: in, Indicates the time prediction coefficient. Indicates a time coefficient predictor. Represents a vector of historical time coefficient matrices. This indicates the number of steps in the historical time coefficient matrix that need to be referenced during prediction. Represents the historical input vector. This indicates the number of historical input steps that need to be referenced during prediction; A spatiotemporal prediction model is constructed based on the time prediction coefficients and the spatial basis functions, and the spatiotemporal prediction model refers to the following formula: wherein, represents the spatio-temporal prediction value of the DPS state at the spatial location , time .

7. A self-adaptive persistent learning time-varying distribution parameter system space-time modeling apparatus, characterized in that, The device is used for modeling and analyzing distributed parameter systems in process industries, including chemical, metallurgical, and energy industries. The adaptive continuous learning spatiotemporal modeling device for time-varying distributed parameter systems includes: The offline data decomposition module is used to collect offline stage state data of the distributed parameter system and perform KL decomposition on the offline stage state data to obtain spatial basis functions and time coefficient matrices. The offline stage state data is the spatiotemporal state data of the system under stable operating conditions collected by multiple spatial point sensors. The offline stage state data includes time series data of temperature, humidity, concentration, flow rate and / or pressure. A spatiotemporal prediction modeling module is used to construct a spatiotemporal prediction model based on the spatial basis function and the time coefficient matrix. The spatiotemporal prediction model includes a time coefficient predictor and a spatial prediction model. The online data analysis module is used to collect online phase status data in response to the distributed parameter system being in the online phase. It uses a spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis to perform multi-scale spatiotemporal nonstationarity analysis on the online phase status data. By calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain, it adaptively generates a spatiotemporal forgetting factor that matches the current dynamic rate of change. The online phase status data is the spatiotemporal status data of the system under dynamic operating conditions collected by multiple spatial point sensors. The online phase status data includes time series data of temperature, humidity, concentration, flow rate and / or pressure. The model dynamic update module is used to determine the model update weights based on the spatiotemporal forgetting factor, dynamically update the spatiotemporal prediction model based on the model update weights and the coupled generative spatiotemporal replay learning mechanism, and return to execute the steps of collecting online stage state data, using the spatiotemporal forgetting mechanism based on spatiotemporal nonstationarity analysis to perform multi-scale spatiotemporal nonstationarity analysis on the online stage state data, and adaptively generating a spatiotemporal forgetting factor that matches the current dynamic change rate by calculating the statistical distribution drift of the prediction residuals of the spatiotemporal prediction model in the spatiotemporal domain, until the distribution parameter system ends the online stage. The spatiotemporal replay learning mechanism generates pseudo-samples by querying the degree of matching with historical data, and mixes them with the online stage state data to generate spatiotemporal data, which is used for updating the spatiotemporal prediction model. The spatiotemporal prediction and analysis module is used to model and analyze the distributed parameter system based on the dynamically updated spatiotemporal prediction model. The spatiotemporal forgetting factor includes a temporal forgetting factor and a spatial forgetting factor; The online data analysis module is further configured to: collect online state data in response to the distributed parameter system being in an online phase, including DPS state data within multiple time windows under the online state; perform spatiotemporal nonstationarity analysis on the online state data to obtain spatiotemporal nonstationary indices of the DPS state data within the time windows, including spatial projection reconstruction error and time prediction residual; construct a fuzzy mapping based on the spatiotemporal nonstationary indices, dividing the numerical ranges of the spatial projection reconstruction error and the time prediction residual into multiple fuzzy subsets covering different intervals; input the numerical values ​​of the spatial projection reconstruction error and the time prediction residual calculated in the online phase into preset membership functions to calculate the membership values ​​of the values ​​belonging to each fuzzy subset, thereby converting rigid scalars into two independent spatiotemporal fuzzy membership vectors; input the spatiotemporal fuzzy membership vectors into the fuzzy inference engine to activate the corresponding spatial adjustment rules and time adjustment rules, and infer the time forgetting factor and spatial forgetting factor.

8. A self-adapting continual learning time-varying distribution parameter system spatiotemporal modeling device, characterized in that, The adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling device includes: a memory, a processor, and an adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling program stored in the memory. The processor is used to run the adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling program, and the adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling program is configured to implement the adaptive continuous learning time-varying distributed parameter system spatiotemporal modeling method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores an adaptive continuous learning spatiotemporal modeling program for a time-varying distributed parameter system. When the adaptive continuous learning spatiotemporal modeling program for a time-varying distributed parameter system is executed by a processor, it implements the adaptive continuous learning spatiotemporal modeling method for a time-varying distributed parameter system as described in any one of claims 1 to 6.

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